## bettyboop8904 2 years ago Can someone please help me with some integral homework before I shoot the crap out of my calculus book pretty please?! Equation in the forum

1. bettyboop8904

$\int\limits_{}^{}\ln (\sqrt[3]{x})$ That is x to the 3 root

2. mathsmind

hi there

3. bettyboop8904

hello = )

4. jim_thompson5910

it might help to think of the cube root of x as x^(1/3)

5. jim_thompson5910

then use the power rule

6. mathsmind

ok do u want me to solve it or should i tell u how to do it

7. bettyboop8904

ok I got as far to as thinking of x^(1/3) lol

8. jim_thompson5910

now use the rule that integral of x^n = (1/(n+1))*x^(n+1)

9. mathsmind

if u solve it i give u medal and if i do so you give me one

10. bettyboop8904

so do u mean put 1/3 in front of the ln of stuff and then put it in front of the entire integral? bc that's what I did and it said it was wrong = (

11. jim_thompson5910

there's no ln involved here

12. mathsmind

u=x^1/3

13. bettyboop8904

ok maybe you should write the whole thing out cuz now you're just confusing me, please, thank you

14. jim_thompson5910

does this rule look familiar |dw:1360297226043:dw|

15. jim_thompson5910

sry the +C is nearly cut off

16. bettyboop8904

no yeah i already know that lol we're in the chapter of integration by parts and there is a ln involved it's in the front of the x^(1/3)

17. satellite73

not to interrupt, but i think the starting point here is $\frac{1}{3}\int \ln(x)dx$ which you do either by parts or by memory

18. jim_thompson5910

oh my bad, i didn't see the ln at the very beginning just thought it was cube root of x

19. mathsmind

its ok

20. satellite73

since $$\ln(x)$$ is a very common function, it might be benificial just to memorize $\int \ln(x)dx=x\ln(x)-x$ you can check by differentiation

21. bettyboop8904

yes that's what i did. oh damn nvm hahaha i think i get it I keep getting it confused that the derivative of ln is 1/x and we don't know the integral of ln yet so we have to do integration by parts lol

22. satellite73

your answer is therefore $\frac{1}{3}\left(x\ln(x)-x \right)$

23. mathsmind

you can use taylor series to integrate this easily

24. mathsmind

but with z=x+1

25. bettyboop8904

you guys were a great help! ty! = )

26. satellite73

i would memorize it just like remembering that $\frac{d}{dx}\sqrt{x}=\frac{1}{2\sqrt{x}}$so while your fellow classmates are integrating by parts, you just write down the answer

27. mathsmind

i won't recommend that method

28. mathsmind

what about$\int\limits \ln e^{^{x ^{2}}}dx$

29. mathsmind

or

30. mathsmind

$\int\limits \ln(x^x)dx$

31. mathsmind

or

32. mathsmind

$\int\limits \ln(x^2+2x+1)dx$

33. mathsmind

so these are 3 examples that can't be used by just memorizing the specific case

34. mathsmind

so basically use integration by parts like ur class mates